Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 162 yellow peas. a. Construct a 95​% confidence interval to estimate of the percentage of yellow peas. b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

Answer 1

Solution :

a ) Given that

n =438 green peas +162 yellow peas = 600

x =162

= x / n =162 / 600 = 0.270

1 - = 1 - 0.270 = 0.730

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.960 * (((0.270 * 0.730) / 600)

= 0.035

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.270 - 0.035< p < 0.270 + 0.035

0.235 < p < 0.305

b ) Given that

n =438 green peas +162 yellow peas = 600

= 0.250

1 - = 1 - 0.250 = 0.750

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.960 * (((0.250 * 0.750) / 600)

= 0.035

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.250 - 0.035< p < 0.250 + 0.035

0.215 < p < 0.285